Arsenal had agreed a £60m deal with City for Sanchez, 28, but it was dependent on them signing Thomas Lemar, who decided to stay at Monaco.
Sanchez played the final 15 minutes of Arsenal’s 3-0 win against Bournemouth.
He received a few jeers as he came on at the Emirates on Saturday.
Sanchez, who returned late back to Arsenal from international duty, was making his first home appearance this season after struggling with injury.
“Alexis Sanchez is very focused on the Premier League and the Europa League and he wants to do well,” Wenger told BBC Sport.
“He is still a bit short physically. He will be quickly back to his best. He will win the fans back, and win them back very quickly.”